|Title:||Unit 6: Connecting Algebra and Geometry through Coordinates|
|Author & Email:||Stephanie Smith, firstname.lastname@example.org, Crystal Godbey, email@example.com|
|Grade Level:||High School Math I|
||Building on their work with the Pythagorean Theorem in the 8th grade to find distances, students use a rectangular coordinate system to verify geometric relationships, including properties of special triangles, quadrilaterals, and slopes of parallel and perpendicular lines.|
|Next Generation Content Standards and Objectives:
||How can we connect Algebra and Geometry through Coordinates?|
|Student will Know:
Students will know how the distance formula is derived from the Pythagorean Theorem.
|Student will Do:
||By the end of this unit, students will be able to formulate explanations showing how the distance formula is derived from the Pythagorean Theorem. To do this, students will first prove the slope criteria for parallel and perpendicular lines. Next, students will use that criterion to solve geometric problems. Lastly, students will use coordinates to prove simple geometric theorems algebraically.|
You can find alternative resources, including websites, at the bottom of each lesson plan.
Formative Assessments are found throughout each lesson. Also, there is a summative quiz that assesses the students on their knowledge of the slope criteria for parallel and perpendicular lines. That quiz can be found in Lesson 3.
||There are two large projects in this unit. The first project can be found in the Are the Stairs Up to Code lesson. In this lesson, students will work in groups to measure the stairwells in their schools. When complete, each student will individually write a letter to an administrator regarding their school’s building codes and if the school meets these codes. The other major projects can be found in the Parking Lot lesson. In that last portion of the lesson (culminating assessment) students are to construct their own parking lots using their conjectures regarding the slopes of parallel and perpendicular lines.|
||Because this is the final unit for Math I, it would be nice to take some time to reflect on the entire Math I course, not only this final unit. The students should have compiled a Math I journal that reflects their triumphs, setbacks, and successes throughout this course. Allow the students to review their individual Math I journals and write a reflection piece regarding Math I in its entirety. Which unit did you enjoy the most? What unit was most challenging for you? What topic did we cover that you felt most accomplished after? Allow the students to share these writing pieces with their language arts teacher and your administrators.|
|Tagged Next Generation Content Standards and Objectives||
|Date Created:||May 31, 2012|
|Date Modified:||August 06, 2012|
|Unit Plan Outline
Prerequisite Lesson: Are the Stairs Up to Code? Slope Review
Lesson 1: Parking Lot: Parallel and Perpendicular Lines on a Coordinate Plane
Lesson 2: Points and Lines and Slopes, Oh My!
Lesson 3: Slope and Parallel/Perpendicular Lines Quiz/Practice
Lesson 4: Connecting the Pythagorean Theorem/Distance Formula
Lesson 5: Let’s Prove It!
Lesson 6: Going Round in Circles
Lesson 7: Working with Sydney
||Many of the lessons in this unit center around real life applications and careers that use mathematical concepts. For example, the lesson Are the Stairs Up to Code asks the students to measure their school’s stairwells and compare their slopes with their county building regulations. Also, the Parking Lot lesson asks students to create parking lot models based on their conjectures regarding the slopes of parallel and perpendicular lines.|
|Key Word Search Fields||
Coordinates, Pythagorean Theorem |